Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-y &= -6 \\ -4x-5y &= -3\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = 4x-3$ Divide both sides by $-5$ to isolate $y$ $y = {-\dfrac{4}{5}x + \dfrac{3}{5}}$ Substitute this expression for $y$ in the first equation. $4x-({-\dfrac{4}{5}x + \dfrac{3}{5}}) = -6$ $4x + \dfrac{4}{5}x - \dfrac{3}{5} = -6$ Simplify by combining terms, then solve for $x$ $\dfrac{24}{5}x - \dfrac{3}{5} = -6$ $\dfrac{24}{5}x = -\dfrac{27}{5}$ $x = -\dfrac{9}{8}$ Substitute $-\dfrac{9}{8}$ for $x$ back into the top equation. $4( -\dfrac{9}{8})-y = -6$ $-\dfrac{9}{2}-y = -6$ $-y = -\dfrac{3}{2}$ $y = \dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{9}{8}, \enspace y = \dfrac{3}{2}$.